Recommended preparation:
Maths 730 (Measure Theory and Integration) and Maths 750 (Topology).
Textbook:
There is no prescribed textbook.
There are huge numbers of books on Functional Analysis, as it is
such a pervasive area of mathematics. Kreyszig's Introductory functional analysis with
applications is easy reading.
Resources:
Lecturers:
Shayne Waldron (first six weeks) and Warren Moors (last six weeks).
Class times:
The class meets
Monday 1 pm am in B11,
Tuesday 1 pm in Eng4501,
Wednesday 1 pm in B05.
Assignments: There will be about six assignments.
Marked assignments will be handed back with model solutions.
Tutorials: We hand out
tutorial questions
each week
(as in Maths 332 and 333). These will give details and examples not fully covered in class.
We may arrange a separate tutorial or just discuss them before, in, or after class.
Assessment: The final grade will be calculated:
30% assignments and 70% final exam, or 100% on the final exam,
whichever is the maximum.
Syllabus:
We will start out with the basics of finite dimensional linear algebra,
and review basic results from earlier courses (e.g., every linear map on
a finite dimensional normed linear space is continuous). We then seek
to extend these ideas, particularly the idea of coordinates,
to the infinite dimensional setting, with Hilbert
spaces being of particular interest. We will certainly do the basics
Riesz representation, Hahn-Banach, open mapping, closed graph, Baire category,
and some type of spectral theorem (the analogue of the fact every Hermitian
matrix is unitarily diagonalisable).
Here is a rough summary of the first few lectures: